Real-world scenario:
You are a manager of a coffee shop and you are trying to decide how many regular and decaf coffee bags to order for the upcoming week. The regular coffee costs $5 each and the decaf coffee costs $4 each. You need a total of 40 bags of coffee and you have a budget of $180. Write a system of equations to represent this scenario and solve for the number of regular and decaf coffee bags to order.
Let x represent the number of regular coffee bags and y represent the number of decaf coffee bags.
Equation 1: x + y = 40 (total number of bags)
Equation 2: 5x + 4y = 180 (total cost)
Solving the system of equations:
Equation 1: x + y = 40
Equation 2: 5x + 4y = 180
Multiply Equation 1 by 4:
4x + 4y = 160
Subtract the modified Equation 1 from Equation 2:
5x + 4y - 4x - 4y = 180 - 160
x = 20
Substitute x = 20 into Equation 1:
20 + y = 40
y = 20
Therefore, the manager should order 20 bags of regular coffee and 20 bags of decaf coffee to stay within budget and fulfill the total number of bags needed.